In Nevada, the fourth state to vote, Trump garners 38-percent support, followed by Carson at 22 percent, Fiorina with 8-percent support, Rubio with 7 percent, and Bush with 6-percent support.

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The poll will be a welcome sign for the Trump campaign, which has seen his rivals begin to catch up in Iowa and New Hampshire, the first two states on the presidential calendar.

The poll also comes as other national surveys show Carson cutting into Trump's lead overall. But the bigwig billionaire still holds double-digit leads over the fast-rising Carson by 16 points in Nevada and 18 points in South Carolina. In both states, they are well ahead of the pack, with the third-place finisher below 10-percent support.

The poll highlights Trump’s popularity among voters when it comes to the economy, immigration and electability.

Sixty-seven percent of respondents in Nevada and 59 percent in South Carolina say the real estate mogul is the best man to handle the economy, which was the top issue for voters in both states.

When asked which candidate would do best on illegal immigration, 55 percent in Nevada and 51 percent in South Carolina chose Trump.

And nearly half of respondents in each state, 47 percent in Nevada and 44 percent in South Carolina, said Trump is the most electable candidate in the GOP field.

Trump also takes the highly coveted white, evangelical vote in South Carolina, which made up two-thirds of its 2012 primary vote, by a 32- to 24-percent margin over Carson.

The CNN/ORC poll surveyed 521 likely Republican voters in South Carolina and 285 in Nevada from Oct. 3 to Oct. 10. The margin of error in South Carolina is 4.5 percent and 6 percent in Nevada.